Hsu's theorem in variance component models
Improving both domain and total area estimation by composition.
In this article we propose small area estimators for both the small and large area parameters. When the objective is to estimate parameters at both levels, optimality is achieved by a sample design that combines fixed and proportional allocation. In such a design, one fraction of the sample is distributed proportionally among the small areas and the rest is evenly distributed. Simulation is used to assess the performance of the direct estimator and two composite small area estimators, for a range...
Improving small area estimation by combining surveys: new perspectives in regional statistics.
A national survey designed for estimating a specific population quantity is sometimes used for estimation of this quantity also for a small area, such as a province. Budget constraints do not allow a greater sample size for the small area, and so other means of improving estimation have to be devised. We investigate such methods and assess them by a Monte Carlo study. We explore how a complementary survey can be exploited in small area estimation. We use the context of the Spanish Labour Force Survey...
Inference on the location parameter of exponential populations
Studentization and analysis of variance are simple in Gaussian families because X̅ and S² are independent random variables. We exploit the independence of the spacings in exponential populations with location λ and scale δ to develop simple ways of dealing with inference on the location parameter, namely by developing an analysis of scale in the homocedastic independent k-sample problem.
Interval estimation in two way nested unbalanced random model.
The present paper deals with interval estimation of variance components in two way nested unbalanced random model. Employing a suitable transformation a statistic has been developed and its distribution is well approximated by chi-square. The confidence intervals for variance components and the simultaneous confidence interval for their ratios have been derived.
Inverting covariance matrices
Some useful tools in modelling linear experiments with general multi-way classification of the random effects and some convenient forms of the covariance matrix and its inverse are presented. Moreover, the Sherman-Morrison-Woodbury formula is applied for inverting the covariance matrix in such experiments.
L'analyse de covariance mise en question
Linear model with inaccurate variance components
A linear model with approximate variance components is considered. Differences among approximate and actual values of variance components influence the proper position and the shape of confidence ellipsoids, the level of statistical tests and their power function. A procedure how to recognize whether these diferences can be neglected is given in the paper.
Minimum Norm Quadratic Estimators of Variance Components.
Minimum variance quadratic unbiased estimation of variance components
Modified minimax quadratic estimation of variance components
The paper deals with modified minimax quadratic estimation of variance and covariance components under full ellipsoidal restrictions. Based on the, so called, linear approach to estimation variance components, i. e. considering useful local transformation of the original model, we can directly adopt the results from the linear theory. Under normality assumption we can can derive the explicit form of the estimator which is formally find to be the Kuks–Olman type estimator.
Monotonicity properties of statistical procedures for an increasing number of observations or a decreasing number of parameters, especially Anova procedures
New progress in enumeration of mixed models.
Note on the ANOVA of a completely confounded factorial experiment
The purpose of this paper is to present a modern approach to the analysis of variance (ANOVA) of disconnected resolvable group divisible partially balanced incomplete block (GDPBIB) designs with factorial structure and with some interaction effects completely confounded. A characterization of a factorial experiment with completely confounded interaction is given. The treatment effect estimators and some relations between the matrix F of the reduced normal equations and the information matrix A are...
Note on the estimation of parameters of the mean and the variance in -stage linear models
The paper deals with the estimation of the unknown vector parameter of the mean and the parameters of the variance in the general -stage linear model. Necessary and sufficient conditions for the existence of the uniformly minimum variance unbiased estimator (UMVUE) of the mean-parameter under the condition of normality are given. The commonly used least squares estimators are used to derive the expressions of UMVUE-s in a simple form.
On a distance between estimable functions.
In this paper we study the main properties of a distance introduced by C.M. Cuadras (1974). This distance is a generalization of the well-known Mahalanobis distance between populations to a distance between parametric estimable functions inside the multivariate analysis of variance model. Reduction of dimension properties, invariant properties under linear automorphisms, estimation of the distance, distribution under normality as well as the interpretation as a geodesic distance are studied and...
On admissibility of linear estimators in models with finitely generated parameter space
The paper refers to the research on the characterization of admissible estimators initiated by Cohen [2]. In our paper it is proved that for linear models with finitely generated parameter space the limit of a sequence of the unique locally best linear estimators is admissible. This result is used to give a characterization of admissible linear estimators of fixed and random effects in a random linear model for spatially located sensors measuring intensity of a source of signals in discrete instants...
On Classes of Estimators of the Variance Function of a Linear Estimator.
On conditional independence and log-convexity
If conditional independence constraints define a family of positive distributions that is log-convex then this family turns out to be a Markov model over an undirected graph. This is proved for the distributions on products of finite sets and for the regular Gaussian ones. As a consequence, the assertion known as Brook factorization theorem, Hammersley–Clifford theorem or Gibbs–Markov equivalence is obtained.
On geometry of the set of admissible quadratic estimators of quadratic functions of normal parameters
We consider the problem of admissible quadratic estimation of a linear function of μ² and σ² in n dimensional normal model N(Kμ,σ²Iₙ) under quadratic risk function. After reducing this problem to admissible estimation of a linear function of two quadratic forms, the set of admissible estimators are characterized by giving formulae on the boundary of the set D ⊂ R² of components of the two quadratic forms constituting the set of admissible estimators. Different shapes and topological properties of...